Instructions
Teach any Pokemon "Surf" and "Strength." Make sure you have at least 50 Ultra Balls in the "Pokeballs" section of your "Bag." Catch a Pokemon and teach it Dragon-, Ice- and Ghost-type moves, which are super effective on Giratina. Train this Pokemon to Level 50.
Beat all the Galatic Members at the Galatic Hideout. Navigate through Mt. Coronet. Once you exit Mt. Coronet, you will find a portal to the Distortion World. Enter the portal and speak to "Cynthia," the Pokemon League Champion.
Use the disappearing and reappearing platforms to get to the end of the Distortion World. Defeat Cyrus's Houndoom, Crobat, Gyarados, Honchkrow and Weavile. After you defeat Cyrus, you will speak to Cynthia again. Go farther into the Distortion World until you stand before Giratina. Save your game just in case you fail to catch Giratina the first time.
Press "A" to get into battle with Giratina. Use Ice-, Ghost- and Dragon-type moves on the Giratina. Get the Legendary Pokemon's health as close to one hitpoint as possible. Use an Attack to give the Giratina a status effect like "Sleep." A status effect will increase the chances of you capturing Giratina.
Toss Ultra Balls at the Giratina until you catch it. If you run out of Ultra Balls, restart "Pokemon Diamond" to try to catch it again.